Stability Analysis And Control Of LPV System With Time Delay

Generally,most practical systems are nonlinear and time-varying and it is hard to describe dynamics by exact mathematical models,which causes errors between the actual controlled object and mathematical models,even has an impact on systematic analysis and control.The problem of mathematical modeling of complicated nonlinear system are effectively solved with the emergence of linear parameter varying system(LPV system)which is mainly to define the system parameters reflecting the nonlinear and time-varying characteristics as a time-varying parameter vector.At each fixed time,the state values of the time-varying parameter vector can be measured,and then address the systematic analysis and synthesis with appropriate control method.In addition,time delay restricts the performance of a system.Taking the influence of time delay into account is more close to the practical physical process of the system.Therefore,to make our research work more practical,we investigate the continuous LPV system with time-varying delay in this paper.Considering present research,although the theory of linear parameter varying system with time delay attract the wide attention of many scholars,it is of large limitations for the research about LPV system with time delay,especially the problems of stability analysis and controller design.Most existing researches got a higher conservative conclusion without fully considering the influence of time delay.In view of the above analysis,the main research work of this paper is as follows:First,we present a novel idea to reduce the common existing higher conservation about continuous LPV system with time varying delay.We add delay information in the Lyapunov function construction by the time delay partition technique and the interactive convex combination method and delay dependent stability conditions are derived when the time-varying delay is partitioned into 2 parts and m(m ?2)parts,which develops a lower conservative stability criterion.The relationship between the number of the delay partition and the conservation is also presented in this paper as well as computational complexity.Second,this paper examines the controller design problem of LPV system with time delay.Based on the less conservative stability conclusions,the sufficient conditions for the existence of state feedback controller of LPV system with time delay are derived by the linear matrix inequality tool.Then,we get the controller gain through the feasp solver of LMI toolbox in Matlab software.The simulation results validate the effectiveness and feasibility of the designed state feedback controller.